Problem: Simplify to lowest terms. $\dfrac{48}{64}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 48 and 64? $48 = 2\cdot2\cdot2\cdot2\cdot3$ $64 = 2\cdot2\cdot2\cdot2\cdot2\cdot2$ $\mbox{GCD}(48, 64) = 2\cdot2\cdot2\cdot2 = 16$ $\dfrac{48}{64} = \dfrac{3 \cdot 16}{ 4\cdot 16}$ $\hphantom{\dfrac{48}{64}} = \dfrac{3}{4} \cdot \dfrac{16}{16}$ $\hphantom{\dfrac{48}{64}} = \dfrac{3}{4} \cdot 1$ $\hphantom{\dfrac{48}{64}} = \dfrac{3}{4}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{48}{64}= \dfrac{2\cdot24}{2\cdot32}= \dfrac{2\cdot 2\cdot12}{2\cdot 2\cdot16}= \dfrac{2\cdot 2\cdot 2\cdot6}{2\cdot 2\cdot 2\cdot8}= \dfrac{2\cdot 2\cdot 2\cdot 2\cdot3}{2\cdot 2\cdot 2\cdot 2\cdot4}= \dfrac{3}{4}$